I'm an acupuncturist, and although I don't really treat animals I have treated my mums dog in the past for arthritis and I have to say I didn't really know what I was doing but amazingly she sat still for the treatment and seemed to get up better for a while afterwards. Its not something I was able to do frequently though.
I know other colleagues who treat animals more frequently with good success so it would be worth making sure the person doing the acu has had some formal training with dogs & acu - i think vets sometimes do it too.
With regards to the severity, acupuncture could help regardless but the more severe the pain, the less likely you are to get rid of it completely but it should still help lower the pain level. Acu & arthritis is quite well researched in humans and the majority of my patients fit into this category, but it is something you need to keep doing so you may want to factor this in. The goal of any treatment is to reduce the symptoms as much as possible and for as long as possible, but initially more frequent treatments are needed which are then usually spaced out. I have some patients who only come once every 3 months and that keeps the pain at bay or at a manageable level.
Hope this helps.